A business name is not necessarily a trademark. It would depends how it's used. The requirement on business names in most states (and Quincy is right, the state/country is important) is that it be distinct from other entities. The basis of trademarks is that they not be likely to be confused with another (put very simply).
For example, there's a company called "Doctor's Associates." There are lots of businesses that use Doctor's Associates in some form. Most are probably medical businesses and have trademark rights for using that. The company called Doctor's Associates does business under the mark SUBWAY. You'd be ill-advised to use SUBWAY as a mark or a business name if you're selling sandwiches.